Green's Function Approach to Entanglement Entropy on Lattices and Fuzzy Spaces

TL;DR

This paper introduces a Green's function method to compute Rényi entanglement entropy for coupled oscillators on lattices and fuzzy spaces, providing explicit formulas and potential for including interactions.

Contribution

Develops a Green's function framework for calculating entanglement entropy on lattices and fuzzy spaces, with explicit formulas and perturbative extension to interacting systems.

Findings

Explicit Green's function construction for Rényi entropy

New formula for entanglement entropy derived

Framework for including interactions perturbatively

Abstract

We develop a Green's function approach to compute R\'{e}nyi entanglement entropy on lattices and fuzzy spaces. The R\'{e}nyi entropy resulting from tracing out an arbitrary collection of subsets of coupled harmonic oscillators is written as zero temperature partition function generated by an Euclidean action with $n$-fold step potential. The associated Green's function is explicitly constructed and an alternative new formula for the R\'{e}nyi entropy is obtained. Finally it is outlined how this approach can be used to go beyond the gaussian state and include interaction by writing a perturbative expansion for the entanglement entropy .